Method and apparatus for the correction of signal-pairs

ABSTRACT

Method and apparatus for correcting signal-pairs from vectors that represent inphase signals (I) and quadrature signals (Q). The values for correction of the amplitude error α and phase error δ are determined by calculating the most probable correction values of offsets from a center point of the signal-pairs using signal probes from the stream of the inphase and quadrature signals. The amplitude error α and phase error δ are calculated corrected as a function of the signal probes only after a preceding correction of the center point.

This application is a 371 of PCJ/DE95/01125 filed Aug. 24, 1995.

The invention relates to a method and an apparatus for the correction ofsignalpairs, comprising inphase (I) and quadrature signals (Q) which arerepresentable as vectors.

STATE OF THE ART

Analog or digital perpendicular signal-pairs in particular areapplicated, where two signals are transferred at the same time by meansof only one carrier-signal, for instance at the television with themodulation of the carrier for the color signal at the PAL-standard, orat the vector modulation, but also, where the signal spectra areconverted into another frequency range, such as in radio signals, theprocessing of radar signals and the sonometrie. The method of theinvention and the apparatus thereby advantageously can be utilized forthe correction of angular modulated signals.

Due to non ideal components having a tolerance linear distortions of thebase band signals arise, among other things through mismatch of theamplitudes and phases, the offset of the DC-signal and the frequency, aswell as through non linear distortions caused by crosstalk andintermodulation.

Correction devices take remedial measures, which are detectingsystematic and statistical errors of the perpendicular pair of signalsby means of suitable detectors and generating correction signalsthereof, in order to adjust the errors through feedback.

In EP 473 373 a system for calibrating a homodyne receivers isdescribed, in order to adjust the error of the phase in theHF-front-end. The described system has the disadvantage, that theoperation is interrupted in intervals for the injection of an auxiliarycarrier and that the reference signal distinguishes from the receivedsignal, so that only an approximated correction of the phase is takingplace.

In EP 343 273 in a process following the HF-front-end, the whole lineardistortions named above, with exception of the frequency offset, aredetected and adjusted by multiple underlying feedback's. Thedisadvantage of this procedure is the concatenation of the controlvariables and the need of control permanently increased therewith, aswell as the risk of instability associated therewith. This state of theart a separately and commutative, separate of each other feasiblecorrection of the DC-offset, of the amplitude- and phase-error is to begathered. The solution is based on a calculation of most probably valuesinsofar, as DC-signal parts are determined for the calculation of valuesfor correction.

In EP 595 278 the determination of the whole error values of I- andQ-signals at homodyne receivers by a calculation of most probably valuesis claimed, e.g. by a linear regression (see I. O. Kerner "BesterKegelschnitt durch n Punkte" ZAMM 59, pp. 396-397, 1979). Thedisadvantage of the procedure is the complex calculational effort forthe solution of a square matrix for five unknown parameters of anellipsis, which is also not revealed in that patent specification.

From EP 598 277 and DE 39 38 643 a method and an apparatus for theoffset correction is known. Thereby it is required that the correctionof the ellipsis has taken place before.

For the correction of the offset of the center point the coordinates ofthe center point of two I- and Q-signals being in quadrature anddisplaced about the center point are determined by means of calculationof the most probably values such, that lines of centers of gravity areformed and a common intersection point will be determined. For this, anumber of differences of square radii of respective two successivepoints are minimized and subtracted of the I- and Q-signals. Thelinearization and minimization of the function is also carried outaccording to I. O. Kerner. Such a solution is showing a comparativelygreat deviation of the actual centers because of the finite precision ofcalculating of the executive arithmetic units. In particular therounding errors are greatly increasing with growing distortion.

In EP 595 277 the frequency-offset of the local oscillator at homodynereceivers is claimed, which causes a superimposed rotation of thevector, represented by the perpendicular pair of signals in theCartesian I-, Q-plane, so that the probability of the top of the vectorbeing at a defined place is regularly distributed to the circumferenceof the ellipse.

In U.S. Pat. No. 5,165,051 a method and an apparatus for determinationof the amplitude, the phase and the frequency of a pair of signals isdisclosed, comprising inphase (I) and quadrature signals (Q) beingrepresentable as vectors. By means of the method of the minimum squarederrors ("Least Square Estimation"--LMS) the signal parameters arecalculated from signal probes. The LMS method is a calculation of mostprobable values having a little calculational effort for filtering theperiodical oscillations from a signal blotted out with noise. Using thecalculated signal parameter of the periodical part of the signal a localoscillator is controlled, which parameter of the periodical part of thesignal a local oscillator is controlled, which signal is blotted outdirectly with the inphase signal (I) and with the quadrature signal (Q)using a phase shift of 90 degree. So, relatively precise the carriersignal can be determined, but only future signals can be corrected. Thecurrent signal used for the calculation of the signal parameter staysunchanged. For this reason, at continuous signals the error could besmall, but because of the feedback of the signal there is danger ofresidual oscillations of the system.

OBJECT OF THE INVENTION

Object of the invention has been showing a method and an apparatus forthe correction of signal-pairs, comprising inphase (I) and quadraturesignals (Q) which are representable as vectors. Thereby, the values forcorrection should be calculated by means of a calculation of the mostprobably values among utilization of signal probes from the signalstream. In order to avoid rest oscillations, the correction should notbe performed with a feedback system. In the method the calculationaleffort should be kept as low as possible.

INVENTION

For the solution of this object the invention now provides, that after apreceding correction of the offset of the center point the error of theamplitudes α and the error of the phases δ is carried out. Theseparameters can be calculated by the matrix equation ##EQU1## whereby atleast respective three signal probes Q'_(k) and I'_(k) already beingcenter point corrected are taken from the signal stream.

According to the invention the system of equations for the correction ofthe amplitude error a and the phase error δ is based upon an equation ofa circle centered in the origin and its transformation to a function ofan ellipse under retention of one of the signals I or Q as a referencesignal. The minimum number of three signal probes Q'_(k) and I'_(k)(n,p≧3) hereby emerges from the necessity of the mathematicaldetermination of the equation systems.

The calculational effort could be greatly minimized both by theseparation and the order of the methods (first the calculation of theoffset of the center point and then the calculation of the errors of theamplitudes and the phases), as well as by the reduction of the equationsystems. Thereby the claimed form of the calculation of the mostprobably values can only be used with the separation and the order ofthe procedures being inventive together with the calculation of the mostprobably values.

For the correction of the center point several methods are conceivable.In comparison with the calculation of the parameter of the ellipse theoffset of the center point has to be calculated less frequently, sincethe disruptive factor varies only over a longer period. Therefore, thedetermination of the offset of the center point has to be performed lessfrequently, so that an optimal solution isn't as necessary forminimizing the calculational effort, such as in the method for thecalculation of the errors of the amplitudes and the phases.

The combination is particularly advantageously using a further newapproach for the determination of the offset of the center point.Hereby, an equation of a circle will be transformed and linearized. Theparameters of the circle are optimized in such a manner, that aresulting circle is best fitted in the crowd of sample values arrangedas an ellipse. Then the offset of the center point will be calculated bythe matrix equation ##EQU2## using signal probes I_(I), from theuncorrected signal stream of the inphase signal (I) and using signalprobes Q_(I), from the uncorrected signal stream of the quadraturesignal (Q). By using this 3×3 equation system the calculational effortcan be considerably minimized.

Thereby, that the offset of the center point is compensated alreadybefore the errors of the amplitudes/phases, the order of magnitude ofthe values is considerably smaller and is always situated in apredictable range. The bit width and the expenditure for the arithmeticunits involved can be held lower by this having an equal precision.Besides the resulting signal quality is essentially improved.

Compared to the methods described in EP 598 277, in which the ellipse istipped over first and is corrected to a circle subsequently, through theinvention a distinctive improvement of the quality could be achieved.The methods basically differ from each other to the effect, that in theinvention the calculation of most probably values is not used for thedetermination of the point of intersection, but for the calculation ofthe coefficients of an optimal adapted circle.

The technical implementation of the apparatus according to claim isdefined by the system of equations. The construction of an concreteapparatus according to the claims 5 to 8 is possible easily for the manskilled in the art by means of a digital signal processor or anintegrated circuit specialized for the applicant (ASIC).

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

In the following the invention will be illustrated in details by meansof the figures:

FIG. 1 shows in form of a circuit block diagram the generation of thedistorted I- and Q-signals (3,4) e.g. by a HF-front-end-module (2) of ahomodyne receiver from the input signal (1) and an apparatus for thecorrection (7) with the corrected signals (5,6), I" and Q".

FIG. 2 shows as a signal flow chart the correction of the DC-offset inuniversally valid form with the arithmetic unit (9) for thedetermination of the center point Qm and Im.

FIG. 3 shows as a signal flow chart the correction of the ellipticity inuniversally valid form with the arithmetic unit (11) for thedetermination of the coefficients for the correction.

In the FIG. 1 as an example a homodyne receiver (2) is shown. The inputsignal (1) arriving from an antenna is amplified and blot out in twomixers with the perpendicular pair of signals of a local oscillator. Thefrequency of oscillation thereby is located in the spectrum to bereceived. The undesired results of the mixed signals, arising in the lowfrequency range, are separated through filters. The invention is basedupon the realization, that the perpendicular low-frequency pair ofsignals (3,4) such generated is represented by a rotating vector in theCartesian I-, Q-plane. With a pure angular modulation the top of thevector of the undistorted and undisturbed pair of signals are lying on acircle, whose center is identical to the origin of the Cartesian I-,Q-plane. By the linear distortions described before the center point ofthe circle is displaced from the origin and the circle is distorted toan ellipse.

In the FIG. 2 the signal flow for the removal of the distortion causedby the DC-offset is shown. The DC-offset is represented by adisplacement of the center point of the rotating vector in the CartesianI-, Q-plane, so that for the correction of the offset the center of thiselliptical I-, Q-signal has to be determined. The invention providesdetermining these center point by calculation of most probably values inthe arithmetic unit (9) for a circle instead of an ellipse from samplesof the measured I- and Q-signals. This method is very exact inparticular then, if through the frequency-offset of the local oscillatormentioned at the beginning a blot out rotation of the vector is broughtin and by this the probability of the top of the vector being at adefined place on the circumference of the ellipse is regularlydistributed. By subtraction of the center point from the measured I- andQ-signal (3,4), the distorting the DC-offset will be removed.

In the FIG. 3 the signal flow for the correction of the ellipticity isshown. The parameters of the ellipse are determined from samples of theI- and Q-signal freed from the DC-offset by calculation of most probablyvalues in the arithmetic unit (11) and the elliptical distortion iscanceled. With it, the linear corrected I- and Q-signals (5,6) areprepared for further processing.

The methods for the correction of the DC-offset and the ellipticaldistortion using the method of the calculation of most probably valuescan be performed independently from each other, because thedetermination of the DC-offset is valid by the assumption of an optimalfitted circle. Thereby, that first the removment of the DC-offset andsubsequently the correction of the ellipticity is taken place, thecalculational effort can be reduced. If the whole values for correctionare determined using only one calculation of most probably values byapplication of the linear regression, a system of equations having a5×5-matrix has to be dissolved. With the division and order of themethods for correction according to the invention the calculationaleffort is reduced to the solution of two independent equation systemseach having a 3×3-matrix and the rounding error is minimized. At thesolution of the system of equations having the 3×3-matrix for thedetermination of the DC-offset an auxiliary value (H) is left beingproportional to the signal power.

This is a further advantage of the procedure, since without specialadditional measure the signal power can be determined, which is anindispensable size in modern communication devices.

An example for the method for the correction of the DC-offset is shownin the FIG. 2 and is described in the following:

The set-up for the arrangement of the matrix (equation 2) for theimplementation of a linear regression is an universally valid equationof a circle (equation 3) and their transformation (equation 4).

    r.sup.2 =(Q-Qm).sup.2 +(I-Im).sup.2                        (3)

    0=Q.sup.2 +I.sup.2 -2·Q·Qm-2·I·Im+H(4)

The sums will be calculated respective from I samples of a pair ofsignals, whereby the samples are taken from a coherent time interval, inthat a change of the parameters to be determined appears to beneglectable small.

The DC-offset is characterized by the center point Qm and Im of thecircle. With the auxiliary variable H the signal power, theRadio-Signal-Strength-lndicator RSSI, can be determined through theequation 5.

    RSSI=Qm+Im-H                                               (5)

In the FIG. 2 is further shown, how the DC-offset is removed by thesubtraction of the correction values Im and Qm from the measured I- andQ-signals. This corresponds to the displacement of the center point ofthe ellipse into the origin of the Cartesian I-, Q-plane.

The subsequent compensation of the ellipticity is simplified by thefact, that the center point of the ellipse is situated in the origin ofthe coordinates.

An example for the method according to the invention for the correctionof the ellipticity is shown in FIG. 3 and will be described in thefollowing:

The set-up for the arrangement of the matrix (equation 1) for theimplementation of the linear regression is an equation of a circlecentered in the origin (equation 6) and its transformation (equation 7).The Q-signal will be kept as a reference signal.

The I'-signal being set perpendicular to the Q'-signal in equation 6 issubstituted by the measure I'- and Q'-signals, so that the amplituderatio a and the phase error δ is inserted into the system of equations.An corresponding set-up under retention of the I-signals as a referencesignal is equally good. ##EQU3##

The sums are calculated respective from K samples of a pair of signals,whereby the samples are taken from a coherent time interval, in that achange of the parameters to be determined appears to be neglectablesmall.

With the lower vector element of equation (2) the signal power, theRadio-Signal-Strength-Indicator RSSI (r²), can be determined.

I claim:
 1. A method for the correction of the amplitude α and phaseerror δ between signal-pairs which comprise inphase signal (I) andquadrature signal (Q) which represent vectors, and in which the valuesfor correction are determined by calculating most probable correctionvalues of offsets from a center point of the signal-pairs using signalprobes I'_(k) from the signal stream of the inphase signal (I) andsignal probes (Q'_(k)) from the signal stream of the quadrature signal(Q) followed by calculating corrections of the signals as a function ofsaid calculated most probable values, the method comprising the steps ofcorrecting the offsets from said center point, and calculating andcorrecting the amplitude α and the phase δ as a function of said signalprobes I'_(k) and Q'_(k) only after a preceding correction of theoffsets from the center point.
 2. Method as claimed in claim 1,characterized in that the amplitude error α and the phase error δ arecalculated by means of the matrix equation ##EQU4## whereby r is theradius of the circle formed by the signal probes I'_(k) and Q'_(k)represented as vectors and p is the number of signal probes taken fromthe signal stream for calculation of the matrix equation, and whereby atleast three signal probes Q'_(k) and I'_(k) are taken from the signalstream.
 3. A method as in claim 1 or 2 characterized in that thecorrection values of the offset of the center point are calculated as afunction of signal probes I_(I) from the uncorrected signal stream ofthe inphase signal (I) and signal probes Q_(I) from the uncorrectedsignal stream of the quadrature signal (Q) by means of the matrixequation ##EQU5## whereby H is a value which is proportional to thesignal power and n is the number of signal probes taken from the signalstream for calculation of the matrix equation, and whereby at leastthree signal probes Q_(I) and I_(I) are taken from the signal stream. 4.A method as in claim 1 and further comprising the step of providing saidinphase signal (L) and quadrature signal (Q) from a homodyne receiver.5. Apparatus for the correction of signal-pairs of, which are as inphase(I) and quadratur signals (Q) representable as vectors, comprising anarithmetic unit (8) for calculation and correction of the offset of thecenter point and an arithmetic unit (9) for calculation and correctionof the amplitude error α as well as of the phase error δ by means of acalculation of most probably values using signal probes I'_(k) from thesignal stream of the inphase signal (I) and signal probes Q'_(k) fromthe signal stream of the quadrature signal (Q), characterized in thatthe arithmetic unit (8) for calculation and correction of the offset ofthe center point is arranged in front of the arithmetic unit (9) forcorrection of the amplitude α and the phase error δ, and that thecalculation of the amplitude α and the phase error δ is carried outusing signal probes I'_(k) and Q'_(k), which are already center pointcorrected.
 6. Apparatus as claimed in claim 5, characterized in that thearithmetic unit (10) is suited for calculation of the amplitude error αby means of the matrix equation ##EQU6## whereby r is the radius of thecircle formed by the signal probes I'_(k) and Q'_(k) represented asvectors and p is the number of signal probes taken from the signalstream for calculation of the matrix equation, and whereby at leastrespective three signal probes Q'_(k) and I'_(k) are taken from thesignal stream.
 7. Apparatus as claimed in claim 5 or 6, characterized inthat the arithmetic unit for calculation of the values for correction Imund Qm of the center point offset (8) using signal probes I_(I) from theuncorrected signal stream of the inphase signal (I) and signal probesQ_(I) from the uncorrected signal stream of the quadrature signal (Q) isdistincted by means of the matrix equation ##EQU7## whereby H is a valuebeing proportional to the signal power and n is the number of signalprobes taken from the signal stream for calculation of the matrixequation, and whereby at least respective three signal probes Q_(I) andI_(I) are taken from the signal stream.
 8. Apparatus as claimed in claim7, characterized in that the arithmetic unit for calculation of thevalues for correction Im und Qm of the center point offset (8) is suitedfor the output of a value H being proportional to the signal power. 9.Apparatus as claimed in claim 8 for the correction of the signal of ahomodyne receiver.
 10. Apparatus as claimed in claim 7 for thecorrection of the signal of a homodyne receiver.
 11. Apparatus asclaimed in one of the claims 5 or 6 for the correction of the signal ofa homodyne receiver.